Multivariate Time Series: Recent Additions to the VARMAX Procedure

Recent advances in computing technology, monitoring systems, and data collection mechanisms have prompted renewed interest in multivariate time series analysis. In contrast to univariate time series models, which focus on temporal dependencies of individual variables, multivariate time series models also exploit the interrelationships between different series, thus often yielding improved forecasts. This paper focuses on cointegration and long memory, two phenomena that require careful consideration and are observed in time series data sets from several application areas, such as finance, economics, and computer networks. Cointegration of time series implies a long-run equilibrium between the underlying variables, and long memory is a special type of dependence in which the impact of a series’ past values on its future values dies out slowly with the increasing lag. Two examples illustrate how you can use the new features of the VARMAX procedure in SAS/ETS® 14.1 and 14.2 to glean important insights and obtain improved forecasts for multivariate time series. One example examines cointegration by using the Granger causality tests and the vector error correction models, which are the techniques frequently applied in the Federal Reserve Board’s Comprehensive Capital Analysis and Review (CCAR), and the other example analyzes the long-memory behavior of US inflation rates.